A boundary element method for viscous gravity currents

The viscous gravity spreading of a blob of fluid on a rigid, horizontal, no-slip surface is studied numerically by applying the boundary-element method to the Stokes equation in plane symmetry. The two-dimensional unsteady solution is obtained by solving the biharmonic equation for the streamfunction in a given domain to obtain the velocity field, which is then used to track the contour. The spreading is developed by letting adhere to the rigid boundary any fluid element set in contact with it. A detailed description of the two-dimensional flow near the head of a viscous gravity current shows a typical rolling motion which characterizes the advancing mechanism of the spreading. In particular, we obtain scaling laws for the shape and size of the current head in good agreement with previously reported experimental data. Attention is also paid to the validation of the numerical method. (C) 1997 by John Wiley & Sons, Ltd.